Choose one value that is in the domain of both y(x) = x² and y² = x and that is greater than
0. Substitute that value into y(x) = x² and y² = x and then simplify. Explain how your answers
help to show that the graph on the left represents a function while the graph on the right
represents a relation. Show your work and use function notation where possible
I

Answers

Answer 1

We take the value 2 for which y(2)=4 and [tex]y^{2}[/tex]=2 and see that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a relation.

Domain is the set of values that a variable can take in an algebraic expression.For the equation y(x)=[tex]x^{2}[/tex], x can take any value from negative infinity to positive infinity so we can say that the domain for x is (-∞,∞). For the equation [tex]y^{2}[/tex]=x, x can take any value greater than or equal to zero. Since x=[tex]y^{2}[/tex] we can't take a negative value for x because squared numbers are always positive, so the domain of x will be [0,∞). The common domain for both the equations is [0,∞). Let us choose a value from this common domain,let's say 2. Then for

y(x)=[tex]x^{2}[/tex]⇒y(2)=4 ...(i)

[tex]y^{2} =x[/tex]=2 then y=±[tex]\sqrt{2}[/tex]...(ii)

A function always has an output variable and one or more input variables.For first equation, y is the output variable and x is the input variable. A relation states that two expressions are equal and one is not dependant on another. For equation (i) y is dependant on x but in equation (ii) both the variables are independant.

Thus we can conclude that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a realtion.

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Related Questions

) consider the following sets s with binary operation ∗. which pairs (s,∗) form a group? if (s,∗) is not a group, which axioms fail? (a) let s be the set of integers z and let a ∗ b

Answers

The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.

The following subsets of Z (with ordinary addition and multiplication) satisfy all but one of the

axioms for a ring. In each case, which axiom fails?

(a) The set S of odd integers.

• The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.

Hence, Axiom 1 is violated.

(b) The set of nonnegative integers.

• If a is a positive integer, then there is no solution of a + x = 0 that is also positive. Hence, Axiom

5 is violated.

In general, to show that a subset S of a ring R, is a subring of R, it is sufficient to show that

(i) S is closed under addition in R

(ii) S is closed under multiplication in R;

(iii) 0R ∈ S;

(iv) when a ∈ S, the equation a + x = 0R has a solution in S.

Let a, b, c ∈ S ⊂ Z with a = rk, b = sk, c = tk.

(i) a + b = rk + sk = (r + s)k ∈ S

(ii) ab = (rk)(sk) = (rsk)k ∈ S

(iii) 0Z = 0 = 0 · k ∈ S

(iv) a = rs ∈ S ⇒ x = −rs ∈ S is a solution ofa + x = 0S

Thus, S is a subring of Z.

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determine the gradient of the line through (-1;2)and (0;-4)

Answers

Step-by-step explanation:

gradient = slope. or similar names.

it expresses the "steepness" of the line. how strongly is it going up or down or ... at all ?

it is represented by the ratio

(y coordinate difference / x coordinate difference)

when going from one point on the line to another.

for these 2 points we see (when going from the first to the second)

x changes by +1 (from -1 to 0).

y changes by -6 (from 2 to -4).

so the slope or gradient is

-6/+1 = -6

To the citizens of the country of Merka, there is no meal
better than a hot dog nestled securely in a hot dog bun. Relish is optional, mustard is not. The hypothetical market for hot dogs in Merka is graphed. Suppose that the price of hot dog buns decreases. Illustrate the impact of this change on the
market by manipulating the appropriate curve or curves.

The equilibrium price it hot dogs:
a) decreases
b) increases
c) remains the same

The equilibrium quantity of hot dogs:
a) increases
b) decreases
c) remains the same

The supply curve shifts:
a) left
b) right

The demand curve shifts:
a) left
b) right

Answers

Based on the price of hot dog buns decreasing, the impact on the market would be the equilibrium price of hot dogs decreases.

The equilibrium quantity of hot dogs decreases.

The supply curve shifts left. The demand curve shifts right.

What happens to the supply curve when prices drop?

When the price of a good like the hot dog duns decreases, supplier will have less incentive to keep making it and so will reduce the quantity supplied to the market. This would mean that the supply curve would shift left.

The demand curve on the other hand would shift right because more people would demand the cheaper hotdogs. The equilibrium price which had fallen would then have to rise.

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I am offering 50 points to answer this and i will do it again and again

Answers

Answer: Between 2 and 7

Answer:

2 to 5

Step-by-step explanation:

i don't know because of i don't this transmission may not have the completed Questionnaire

The midpoint of \overline{\text{AB}} AB is M(-5, 0)M(−5,0). If the coordinates of AA are (-3, 3)(−3,3), what are the coordinates of BB?

Answers

The coordinate of B is (13, -3).

What is Midpoint of line?

Measure of Distance between the two points and then divide by two is known as midpoint of line.

Given that;

The midpoint of the line AB is M (-5, 0).

The coordinate of A is (-3, 3).

Now, Let the coordinate of the point B is (x, y )

Then, By definition of midpoint of two point,

(-3 + x / 2 , 3 + y / 2 ) = (-5, 0)

By compare we get;

-3+ x / 2 = -5

- 3 + x = 2 * 5

- 3 + x = 10

x = 10 + 3

x = 13

And, 3 + y / 2 = 0

3 + y = 0

y = -3

Hence, The coordinate of B (x, y) = (13, -3).

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Answer:  (−7,−3)

Step-by-step explanation: I had the question

19yd.28in.-16yd.31in.​

Answers

Answer:

2yds 33 in

Step-by-step explanation:

Convert everything to the lowest unit(inches) perform the operation and convert back

1 yard = 3 feet
1 foot = 12 in
1 yard = 3feet x 12in = 36 in

19yd, 28in = 19 x 36 + 28 = 684 + 28 = 712 in

16yd, 31 in= 16 x 36 + 31 = 576 + 31 = 607 inches

19yd, 28in - 16yd, 31 in = 712 - 607 = 105 inches

Divide by 36 to get the whole number of yards as quotient
105/36  with remainder of 33

∴ 19yd, 28in - 16yd, 31 in = 105 inches = 2yds 33 inches

We can verify this by converting 2yds 11inches to inches and seeing the values agree

2 yds 33 in = 2 x 36 + 33 = 105

help like rn, like rn rn rn rn , thanks

Answers

Answer:  13π/6    √45

Step-by-step explanation:

[tex]\displaystyle\\\sqrt{11} +3\approx6.32\\\\\pi +3,8\approx6.94\\\\Hence,\\\\6.32 < x,6.94\\\\\frac{61}{10}=6.1 \notin\\\\\frac{13\pi }{6}\approx6.81\in\\\\\sqrt{45}\approx6.71\in \\\\6\frac{1}{9}\approx6.11\notin\\\\\sqrt{83}-3\approx6.11\notin[/tex]

1. There are 2 floors in the initial building.
The workers can build 3 floors each week.
When will the building have 15 more floors
than the INITIAL building?
week #
2
5
0 1
8
2
?

Answers

The number of weeks it would take the workers to build 15 more floors is 5 weeks.

How many weeks would it take to build 15 more floors?

The number of weeks it would take to build 15 more floors can be determined by dividing the number of additional floors by the number of floors the workers can build in one week.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The result of the division process is known as the quotient.

Number of weeks = additional floors ÷ number of floors that can be built in a week

15 ÷ 3 = 5 weeks

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. f(x) = 2x-5; Find f(-8)

Answers

Here , I hope it helps

Answer:

D.  

Theres no need for a explanation :)

Find the 6th term of the arithmetic sequence x+2, -6x-3, -13x-8,...

Answers

X should be he answer

Find the volume of this object.
Use 3 for π.
Volume of a Cylinder
V= πr²h
6 in
10 in
8 in
12 in V≈ [?]in³

Answers

The volume of the object which is made up of two different cylinders will be 383 cubic inches.

What is the volume of a right circular cylinder?

Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be given as,

V = π r²h cubic units

The object is made up of two cylinders. Then the volume of the object will be

V = π x (3)² x 8 + π x (5)² x 2

V = π(72 + 50)

V = 3.14 x 122

V = 383.08 ≈ 383 cubic inches

The volume of the object which is made up of two different cylinders will be 383 cubic inches.

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What are the minimum and maximum temperatures recorded in this table?
Temperature (°C) 11 0 24.2 -32.4 -0.6 0.5

Answers

The minimum temperature recorded is -32.4°C and the maximum temperature is 24.2°C, as seen by basic comparison of values.

What is comparison of values?

The process of comparison of numbers establishes the similarities between two numbers and determines which number is greater, smaller, or equal to another number.

Now, given values :11.0, 24.2, -32.4, -0.6, 0.5

Arranging them in ascending order: -32.4, -0.6, 0.5, 11.0, 24.2Thus, The minimum temperature recorded is -32.4°C and the maximum temperature is 24.2°C, as seen by basic comparison of values.

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Let f(x)=5x-6. Write a function g whose graph is horizontal shrink of the graph of f by a factor of 1/4

The transformed function is g(x)=

Answers

The transformed function is g(x) = 20x-6.

The graph of the function y=f(ax) represents a Horizontal Shrink by a factor of "1/a" of the graph y=f(x) .

To find the horizontal shrink by a factor of 1/a we multiply the input by a .

In the given question

f(x)=5x-6 , is horizontally shrink by a factor of 1/4.

So we multiply the inputs by 4 .

On multiplying the inputs by 4 , we get

f(4x)=5(4x)-6        (...as 5*4=20)

Let g(x) represents the horizontal shrink of f(x) by factor 1/4 , So

g(x)=20x-6

Therefore , the horizontal shrink of the graph of f by a factor of 1/4 is g(x)=20x-6.

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What is the value of (-2) • (7) • (5) • (-4)= Enter your answer as a number, like this: 42

Answers

Answer:

280

Step-by-step explanation:

-2 x 7 = -14

-14 x 5 = -70

-70 x -4 = 280

Answer:

280

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)

According to the order of operations (PEMDAS), when multiplying, work from left to right:

Given expression:

(-2) · (7) · (5) · (-4)

Multiply -2 by 7:

⇒ (-14) · (5) · (-4)

Multiply -14 by 5:

⇒ (-70) · (-4)

Finally, multiply -70 by -4, remembering that if both numbers are negative, the answer is positive:

⇒ 280

Given the line y = -1, write the equation
of the line that is parallel to that line and
passes through (-3,5).

Answers

Answer:

Y+5=0

Step-by-step explanation:

Here,given eqn of line is 0.X+Y+1=0_____(i)

since required eqn is parallel to eqn (i)

0.X+Y+K=0____(ii)

passing point (-3,5)

putting the value of Y

5+K=0

.-.K=(-5)

r required eqn is Y-5=0

Write the following statement in the "if-then" form.
A side of a square measures 3 decimeters if the side's measure is 30 centimeters.
Choose the correct answer below.
OA. If the side of a square measures 3 decimeters, then the side's measure is 30 centimeters.
OB. If the side's measure is 30 centimeters, then the side of a square measures 3 decimeters.

Answers

If the side's measure is 30 centimeters, then the side of a square measures 3 decimeters, is the "if-then" form of A side of a square measures 3 decimeters if the side's measure is 30 centimeters.

A statement with an assumption and a conclusion is known as a conditional statement (also known as an if-then statement). The hypothesis is the initial clause, or "if," part of a conditional statement which is followed by the second, or "then," component of a conditional statement is the conclusion. The theory led to the conclusion.

Thus, option B is correct which is, if the side's measure is 30 centimeters, then the side of a square measures 3 decimeters.

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Help please

An airline charges an extra fee for a checked bag that weighs more than 50 pounds.

Your bag weighs 44.9 pounds.

You have a 2.5 pound hair dryer, a 1.3 pound souvenir, and a 3.6 pound pair of boots.

Which items can you add to the bag without paying the extra fee?

Answers

you can choose any of the 3 items, or any combination of two of the items unless the hair dryer and the boots, because the combined weight is 3.6lb + 2.5lb = 6.1 lb

Which items can you add to the bag without paying the extra fee?

The maximum weight that your bag can have is 50 pounds.

The actual weight of your bag is 44.9 pounds, so if we define x as the weight you can add, then we can write the inequality:

44.9 lb + x ≤ 50lb

Solving the inequality for x, we get:

x ≤ 50lb - 44.9 lb

x ≤ 5.1 lb

Now, the weight of the items are:

hair dryer = 2.5 lb

souvenir = 1.3 lb

boots = 3.6 lb

So you can choose any of the 3 items, or any combination of two of the items unless the hair dryer and the boots, because the combined weight is 3.6lb + 2.5lb = 6.1 lb

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which operation should be used to solve x-5=12

Answers

X-5=12
First you add 5 to both sides (inverse operation)
X-5=12
+5 +5
The 5 cancels out and 12+5 =17
X=17

The required solution of the given expression is x = 17, this is been evaluated by the association of alike terms.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
x - 5 = 12
Now,
Adding 5 on both sides,
x = 17

Thus, The required solution of the given expression is x = 17, this is been evaluated by the association of alike terms.

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2x + 6y = -3
12y = 4x + 20

Answers

Answer: x=-3.25

y=7/12

Step-by-step explanation:

2x + 6y = -3

12y = 4x + 20

6y = -3-2x

6y=20-(-3)+4x-(-2x)

6y=20+3+4x+2x

6y=23+6x

23+6x=-3-2x

23=-3-8x

-8x=26

x=-13/4

x=-3.25

12y = 4(-3.25) + 20

12y=-13+20

12y=7

y=7/12

Find the unit rate for each store. Then decide which offers the better buy.
Store A
5 bottles of juice for $10
Store B
9 bottles of juice for $21

Answers

Store A = 2$ a bottle
Store B = 2.3$ a bottle

Store A is better

4. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate

Answers

The additional information required to prove the SSS Triangle Congruence Postulate is TR = JL

How to state the additional information required?

The congruence postulate is given as:

SSS Triangle Congruence Postulate

The above means that the three sides of the triangles are congruent.

From the figure, the following side lengths are said to be congruent

ST and KL

SR and KJ

For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent

This is represented as:

TR = JL

Hence, the additional information required to prove the SSS Triangle Congruence Postulate is TR = JL

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Solve negative four and one fifth ÷ two and one fourth.

one and 39 over 45
negative one and 39 over 45
negative eight and one twentieth
negative nine and 9 over 20

Answers

Solving the fraction negative four and one fifth ÷ two and one fourth gives; negative one and 39 over 45

How to divide fractions?

We want to divide the fraction negative four and one fifth ÷ two and one fourth. This can be expressed as;

-4¹/₅ ÷ 2¹/₄

Converting to improper fraction gives;

-21/5 ÷ 9/4

= -21/5 * 4/9

= -84/45

3 is a common factor that both numerator and denominator can be divided by to get; -28/15

Expressing the answer as a mixed fraction is; -1 ³⁹/₄₅

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help pls i hslsjdnkxkdjdjdj

Answers

Answer:

(a)20π

(b)74π

Step-by-step explanation:

(a) 2π(5) + (2π(10) × 1/2) = 2π(5) + 2π(5)

= 2π(10)

= 20π

(b) π(5)^2 + (π(10)^2 × 1/2) = 25π + 50π

=75π

Answer: P=20 cm    S=75 cm²

Step-by-step explanation:

We have 2 semicircles with diameter d=10 cm and 1 semicircle with diameter D=20 cm

[tex]\displaystyle\\The\ length \ of \ the\ circle\ is\ \pi D\\The\ length\ of \ the\ semicircle \ is\ \frac{\pi D}{2}[/tex]

[tex]\displaystyle\\a)\\P=2*\frac{\pi d }{2} +\frac{\pi D}{2} \\\\P=\pi d+\frac{\pi D}{2} \\\\P=\pi *(d+\frac{D}{2} )\\P=\pi *(10+\frac{20}{3} )\\\\P=\pi *(10+10)\\\\P=20\pi \ cm\\\\[/tex]

[tex]b)\\\displaystyle\\The\ area \ of \ the\ circle\ is\ \frac{\pi D^2}{4} \\The\ area\ of \ the\ semicircle \ is\ \frac{\pi D^2}{8}\\\\S=2*\frac{\pi d^2}{8} +\frac{\pi D^2}{8} \\\\S=\frac{2*\pi *10^2}8} +\frac{\pi *20^2}{8} \\\\S=\frac{2*\pi*100 }{8} +\frac{\pi *400}{8} \\\\S=\frac{200\pi }{8}+\frac{400\pi }{8} \\\\S=\frac{600\pi }{8} \\\\S=75\pi \ cm^2[/tex]

please help i will mark brainliest if u help

Answers

The correct option is D,  -√15 < -2.75 < -2 3/8 < 15/2.

What is a number line?

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

The value of the given numbers in the decimal form can be written as,

-√15 = -3.873

√15 = 3.873

15/2 = 7.5

-15/2 = -7.5

2 3/8 = 2.375

-2 3/8 = -2.375

Now, let's check in which options are the numbers arranged correctly.

A.) -√15 < -2 3/8 < -2.75 < 15/2

Since -2 3/8 > -2.75. Therefore, this is wrong.

B.) 15/2 < -2 3/8 < -2.75 < -√15

Since -2 3/8 > -2.75. Therefore, this is wrong.


C.) 15/2 < -2.75 < -2 3/8 < -√15

Since 15/2 > -2.75. Therefore, this is wrong.

D.) -√15 < -2.75 < -2 3/8 < 15/2

This is correctly arranged.

Hence, the correct option is D.

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Write 2 decimals that are equivalent to the decimal 9.50?

Please help

Answers

Answer: 9.5 and 9.500

Answer:

One would be 9/5 and another could be 1.8

The tree in Naomi's backyard lost 120 leaves in 12 days.
Which expression below models the change in the number of
eaves per day?
a. 120 ÷ 12
D. -120 ÷ 12
c. 120
-12
d. -120
-12

Answers

The tree in Naomi's backyard lost 120 leaves in 12 days. Therefore, the required expression is A. 120÷12

Hope this helps :)

2x+3y-4;where x=1 and y=-1 answer

Answers

Answer:

-5

Step-by-step explanation:

2x+3y-4

Evaluate for x=1,y=−1

(2)(1)+(3)(−1)−4

(2)(1)+(3)(−1)−4

=−5

Tell whether the figure has line symmetry. If so how many lines of symmetry are there?

Answers

Two lines of symmetry


Keeping the properties of exponents in mind, to what power must you raise the expression 7 to get 7 as the result?

Answers

7*1=7 hope that was the answer you are looking for
Seven to the power of one.

What numbers are a distance of 1/2 unit from 3/5 on a number line?


Select the locations on the number line to plot the points.
info(i rather you draw on the image where the dot goes, if you can)-

picture-------------------------------------------------------

Answers

Step-by-step explanation:

hey try out the questions urself some tips would be to make the 1/2 and 3/5 have the same denominator as those shown in the diagram denominator means the number below

so1/2 x5 would give u 5/10 and 3/5 would give you 6/10

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